Consider an infinitesimally small fluid element with density ρ (of dimensions dx, dy and dz) fixed in space and fluid is moving across this element with a velocity \(\vec{V}=u\vec{i}+v\vec{j}+w\vec{k}\). The net mass flow across the fluid element is given by ______(a) \([\frac{\partial(\rho u)}{\partial x} + \frac{\partial(\rho v)}{\partial y} + \frac{\partial(\rho w)}{\partial z}]dx \,dy \,dz\)(b) \([\frac{\partial(\rho u)}{\partial x} + \frac{\partial(\rho v)}{\partial y} + \frac{\partial(\rho w)}{\partial z}]\)(c) [ρ]dx dy dz(d) \([\frac{\partial(\rho)}{\partial x} + \frac{\partial(\rho)}{\partial y} + \frac{\partial(\rho)}{\partial z}]dx \,dy \,dz\)This question was posed to me in semester exam.This is a very interesting question from Continuity Equation in chapter Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Consider an infinitesimally small fluid element with density ρ (of di

1.	Consider an infinitesimally small fluid element with density ρ (of dimensions dx, dy and dz) fixed in space and fluid is moving across this element with a velocity \(\vec{V}=u\vec{i}+v\vec{j}+w\vec{k}\). The net mass flow across the fluid element is given by ______(a) \([\frac{\partial(\rho u)}{\partial x} + \frac{\partial(\rho v)}{\partial y} + \frac{\partial(\rho w)}{\partial z}]dx \,dy \,dz\)(b) \([\frac{\partial(\rho u)}{\partial x} + \frac{\partial(\rho v)}{\partial y} + \frac{\partial(\rho w)}{\partial z}]\)(c) [ρ]dx dy dz(d) \([\frac{\partial(\rho)}{\partial x} + \frac{\partial(\rho)}{\partial y} + \frac{\partial(\rho)}{\partial z}]dx \,dy \,dz\)This question was posed to me in semester exam.This is a very interesting question from Continuity Equation in chapter Governing Equations of Fluid Dynamics of Computational Fluid Dynamics
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